# 10.1 - 3D Coordinate Systems

- StudyBlue
- North-carolina
- University of North Carolina - Charlotte
- Mathematics
- Mathematics 2241
- Gordon
- 10.1 - 3D Coordinate Systems

**Created:**2016-08-23

**Last Modified:**2017-01-09

*a*is the

*x*-coordinate and b is the

*y*-coordinate

- ordered pair (
*a,b*) - ordered triple (
*a,b,c*)

*a,b*)

- ordered pair (
*a,b*) - ordered triple (
*a,b,c*)

*a,b,c*)

- x = 0
- y = 0
- z = 0

- x = 0
- y = 0
- z = 0

The first-octant is the octant in which all point coordinates are positive. There is no conventional numbering system for the remaining octants.

- x > 0, y > 0, z < 0
- x > 0, y < 0, z > 0
- x > 0, y > 0, z > 0

- x > 0, y > 0, z < 0
- x < 0, y > 0, z > 0
- x > 0, y > 0, z > 0

- x > 0, y > 0, z < 0
- x < 0, y > 0, z < 0
- x < 0, y < 0, z > 0

- x > 0, y < 0, z > 0
- x < 0, y > 0, z < 0
- x < 0, y < 0, z > 0

*x*and

*y*is a _______ in R

^{2}. In three-dimensional analytic geometry, an equation in

*x*,

*y*, and

*z*represents a _______ in R

^{3}

- curve; surface
- surface; surface

- x > 0, y > 0, z < 0
- x < 0, y > 0, z < 0
- x < 0, y < 0, z > 0

**R**

^{3}are represented by the following equation, y = 5?

**R**

^{3}are represented by the following equation, z =

__3__?

- the set of all points in
**R**^{3}whose z-coordinate is__3__. - the set of all points in
**R**^{3}whose y-coordinate is__5__.

**R**

^{3}whose z-coordinate is

__3__.

**R**

^{3}are represented by the following equation, y = 5?

- the set of all points in
**R**^{3}whose z-coordinate is__3__. - the set of all points in
**R**^{3}whose y-coordinate is__5__.

**R**

^{3}whose y-coordinate is

__5__.

Distance |P

_{1}P

_{2}| between points P

_{1}(x

_{1},y

_{1},z

_{1}) & P

_{2}(x

_{2},y

_{2},z

_{2}) is

- |P
_{1}, P_{2}| = √((x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}+(z_{2}-z_{1})^{2}) - |P
_{1}, P_{2}| = √((x_{2}-x_{1})^{2}−(y_{2}-y_{1})^{2}−(z_{2}-z_{1})^{2})

_{1}, P

_{2}| = √((x

_{2}-x

_{1})

^{2}+(y

_{2}-y

_{1})

^{2}+(z

_{2}-z

_{1})

^{2})

_{1},y

_{1},z

_{1}) and Q(x

_{2},y

_{2},z

_{2}) in R

^{3}:

- d = √(x
_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}+(z_{2}-z_{1})^{2}

True or False

_{0},y

_{0},z

_{0}):

- (x
_{0}-x)^{2}-(y_{0}-y)^{2}-(z_{0}-z)^{2}= r^{2}

**(x-x**

_{0})^{2}+(y-y_{0})^{2}+(z-z_{0})^{2}= r^{2}**or**

**x**

^{2}+ y^{2}+ z^{2}= r^{2}- M • ((x
_{1}+x_{2}/2),(y_{1}+y_{2}/2), z_{1}+z_{2}/2)

*C*(

*h, k, l*) & radius

*r*

- (
*x*−*h*)^{2}+(*y*−*k*)^{2}+(*z*−*l*)^{2}=*r*^{2} - (
*x*−*h*)^{2}−(*y*−*k*)^{2}−(*z*−*l*)^{2}=*r*^{2} - (
*x*−*h*)^{3}−(*y*−*k*)^{3}−(*z*−*l*)^{3}=*r*^{5}

*x*−

*h*)

^{2}+(

*y*−

*k*)

^{2}+(

*z*−

*l*)

^{2}=

*r*

^{2}

*x*

^{2}+

*y*

^{2}+

*z*

^{2}=

*r*

^{2}if the is the origin

*O*

^{}

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